Sums of slices in direct sums of Banach spaces; pp. 8–10
PDF | doi: 10.3176/proc.2014.1.03Abstract
Motivated by recent studies on the strong diameter 2 property, we exhibit a simple reason why, in many direct sums of Banach spaces, the arithmetic mean of two slices may have diameter less than 2.
References
1. Abrahamsen, T., Lima, V., and Nygaard, O. Remarks on diameter 2 properties. J. Conv. Anal., 2013, 20, 439–452.
2. Acosta, M. D., Becerra Guerrero, J., and López Pérez, G. Stability results of diameter two properties. J. Conv. Anal. (to appear).
3. Day, M. M. Normed Linear Spaces, Third Ed. Springer, Berlin–Heidelberg, 1973.
http://dx.doi.org/10.1007/978-3-662-09000-8
4. Haller, R. and Langemets, J. Two remarks on diameter 2 properties. Proc. Estonian Acad. Sci., 2014, 63, 2–7.
5. Lindenstrauss, J. and Tzafriri, L. Classical Banach Spaces II: Function Spaces. Springer, Berlin–Heidelberg, 1979.http://dx.doi.org/10.1007/978-3-662-35347-9
